Thread: Calc question

  1. #1
    The Right Honourable psychopath's Avatar
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    Mar 2004
    Where circles begin.

    Calc question

    Was studying for my calculus exam, and came across something in a solution I don't quite understand.

    How does the integral of 2x^2/1+x^2 turn into 2*the integral of 1-(1/1+x^2) (integral bounds are 0 to 1).

    I understand how the 2 moves out of the integral, but I don't know how it turns into 1-(1/...). Is it some sort of rule I missed?
    M.Eng Computer Engineering Candidate
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  2. #2
    Officially An Architect brewbuck's Avatar
    Join Date
    Mar 2007
    Portland, OR
    It is just algebra.

    You can write 1 as (1+x^2)/(1+x^2). So:

    1 - 1/(1+x^2) = (1+x^2)/(1+x^2) - 1/(1+x^2) = (1+x^2-1)/(1+x^2) = x^2/(1+x^2)
    	if (a) do { f( b); } while(1);
    	else   do { f(!b); } while(1);

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